An oxygen sample has a volume of 5 L at 27�C
and 800 torr. How many oxygen molecules
does it contain?
Use PV = nRT and solve for n.
Hint: Then ! mol O2 contains 6.02E23 molecules.
To find the number of oxygen molecules in the sample, we need to use the ideal gas law equation:
PV = nRT
where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given values to the appropriate units:
- Pressure: 800 torr = 800/760 atm (since 1 atm = 760 torr) ≈ 1.05 atm
- Volume: 5 L
- Temperature: 27°C = 27 + 273.15 K ≈ 300.15 K
Now we can plug these values into the ideal gas law equation to find the number of moles (n):
(1.05 atm) * (5 L) = n * (0.0821 L·atm/(mol·K)) * (300.15 K)
Simplifying the equation:
5.25 L·atm = n * 24.675 L·atm/(mol·K)
Dividing both sides by 24.675 L·atm/(mol·K):
n = 5.25 L·atm / 24.675 L·atm/(mol·K)
n ≈ 0.213 mol
Since 1 mole of any gas contains approximately 6.022 x 10^23 molecules (Avogadro's number), we can multiply the number of moles by Avogadro's number to find the number of oxygen molecules:
Number of molecules = (0.213 mol) * (6.022 x 10^23 molecules/mol)
Number of molecules ≈ 1.28 x 10^23 molecules
Therefore, the oxygen sample contains approximately 1.28 x 10^23 oxygen molecules.
To find the number of oxygen molecules in the given sample, we need to use the Ideal Gas Law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
We can rearrange the equation to solve for n:
n = (PV) / (RT)
Now let's plug in the given values:
P = 800 torr
V = 5 L
R (ideal gas constant) = 0.0821 L·atm/(K·mol) (This constant can also be expressed as 8.314 J/(K·mol), depending on the units used for pressure and volume. In this case, we will use the units commonly used in chemistry.)
T = 27°C + 273.15 (convert to Kelvin) = 300.15 K
n = (800 torr * 5 L) / (0.0821 L·atm/(K·mol) * 300.15 K)
Now we can calculate n:
n = (4000 L·torr) / (24.732 L·torr/(K·mol))
Simplifying the units:
n = 161.91 mol
To convert the number of moles to the number of oxygen molecules, we can use Avogadro's number, which is 6.022 x 10^23 molecules/mol.
Number of oxygen molecules = n * Avogadro's number
Number of oxygen molecules = 161.91 mol * (6.022 x 10^23 molecules/mol)
Now we can calculate the number of oxygen molecules:
Number of oxygen molecules = 9.749 x 10^25 molecules
Therefore, the given oxygen sample contains approximately 9.749 x 10^25 oxygen molecules.